Dicot: Difference between revisions
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== Tunings == | == Tunings == | ||
=== Norm-based tunings === | === Norm-based tunings === | ||
{{ | {{Todo|complete section|inline=1}} | ||
=== Tuning | |||
=== Tuning spectrum === | |||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |- | ||
| Line 50: | Line 51: | ||
| '''[[4edo|1\4]]''' || || '''300.000''' || '''Lower bound of 5-odd-limit diamond monotone''' | | '''[[4edo|1\4]]''' || || '''300.000''' || '''Lower bound of 5-odd-limit diamond monotone''' | ||
|- | |- | ||
| || | | || 5/3 || 315.641 || Full comma | ||
|- | |- | ||
| || 9/5 || 339.199 || 2/3-comma | | || 9/5 || 339.199 || 2/3-comma | ||
| Line 64: | Line 65: | ||
| [[17edo|5\17]] || || 352.941 || | | [[17edo|5\17]] || || 352.941 || | ||
|- | |- | ||
| || | | || 45/32 || 358.045 || 2/5-comma | ||
|- | |- | ||
| [[10edo|3\10]] || || 360.000 || | | [[10edo|3\10]] || || 360.000 || | ||
| Line 72: | Line 73: | ||
| || 5/4 || 386.314 || Untempered tuning | | || 5/4 || 386.314 || Untempered tuning | ||
|- | |- | ||
| '''[[3edo|1\3]]''' || || '''400.000''' || '''Upper bound of 5-odd-limit, <br>5-limit 9-odd-limit diamond monotone''' | | '''[[3edo|1\3]]''' || || '''400.000''' || '''Upper bound of 5-odd-limit, <br>and 5-limit 9-odd-limit diamond monotone''' | ||
|} | |} | ||
<nowiki/>* Besides the octave | <nowiki/>* Besides the octave | ||
Revision as of 09:55, 11 January 2026
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- This page is about the regular temperament. For the ploidacot signature, see Ploidacot/Dicot.
Dicot is an exotemperament that tempers out 25/24. It is also the first fully prototypical dicot temperament. It tempers 6/5 and 5/4 into the same neutral third interval, which, when the fifth is tuned pure, is sqrt(3/2). It is useful to represent the structure of 5-limit harmonies without fully representing them in its greater accuracy, with mos scales 3L 4s and 7L 3s.
It can be extended by tempering out 15/14 and 36/35 in the 7-limit, though this could turn the 3L 4s mos into a 4L 3s mos. This makes 7/6 and 9/7 equated to the neutral third, viewing 6:7:9 as a tertian chord.
Another notable extension of dicot is decimal, which splits the octave in two for 7/5~10/7 by tempering out 50/49, and equates 7/6 and 8/7 to the tritone complement of 5/4~6/5, neutralizing the 6:7:8 chord as well. This represents the structure of 7-limit harmonies in a way that is not based on tertian harmony and a heptatonic system, but rather a decatonic one.
For technical data, see Dicot family #Dicot.
Interval chain
In the following table, odd harmonics 1–9 are labeled in bold.
| # | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 351.1 | 5/4, 6/5 |
| 2 | 702.2 | 3/2 |
| 3 | 1053.3 | 9/5, 15/8 |
| 4 | 204.3 | 9/8 |
* In 5-limit CWE tuning
Tunings
Norm-based tunings
|
Todo: complete section |
Tuning spectrum
| Edo generator |
Eigenmonzo (Unchanged-interval)* |
Generator (¢) | Comments |
|---|---|---|---|
| 1\4 | 300.000 | Lower bound of 5-odd-limit diamond monotone | |
| 5/3 | 315.641 | Full comma | |
| 9/5 | 339.199 | 2/3-comma | |
| 2\7 | 342.857 | Lower bound of 5-limit 9-odd-limit diamond monotone | |
| 27/20 | 343.910 | 3/5-comma | |
| 7\24 | 350.000 | 24c val | |
| 3/2 | 350.978 | 1/2-comma | |
| 5\17 | 352.941 | ||
| 45/32 | 358.045 | 2/5-comma | |
| 3\10 | 360.000 | ||
| 15/8 | 362.756 | 1/3-comma | |
| 5/4 | 386.314 | Untempered tuning | |
| 1\3 | 400.000 | Upper bound of 5-odd-limit, and 5-limit 9-odd-limit diamond monotone |
* Besides the octave